From 96b5475447d3e20d2ac90fd5ddb032d490ec997d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Matt=C3=A9o=20Delabre?= <contact@matteodelabre.me>
Date: Thu, 24 Dec 2015 12:21:29 +0100
Subject: [PATCH] :bulb: Generalize polygon systems

---
 scripts/ifs.js | 23 ++++++++++++++++++-----
 1 file changed, 18 insertions(+), 5 deletions(-)

diff --git a/scripts/ifs.js b/scripts/ifs.js
index df58ae2..c3c2408 100644
--- a/scripts/ifs.js
+++ b/scripts/ifs.js
@@ -12,6 +12,20 @@ const polygonTransforms = (vertices, frac) => vertices.map(
     )
 );
 
+const regularVertices = count => {
+    var step = 2 * Math.PI / count;
+    var initial = -Math.atan(Math.sin(step) / (Math.cos(step) - 1));
+    var result = [];
+
+    for (var i = 0; i < count; i += 1) {
+        var current = step * i + initial;
+
+        result.push([Math.cos(current) * 10, Math.sin(current) * 10]);
+    }
+
+    return result;
+};
+
 export const barnsley = [[
     linearTransform(0, 0, 0, 0.16, 0, 0),
     linearTransform(.85, .04, -.04, .85, 0, 1.6),
@@ -21,8 +35,7 @@ export const barnsley = [[
     .01, .85, .07, .07
 ]];
 
-export const sierpinski = [polygonTransforms([
-    [.866, .5],
-    [-.866, .5],
-    [0, -1]
-], 1 / 2), [1 / 3, 1 / 3, 1 / 3]];
+export const sierpinski = [
+    polygonTransforms(regularVertices(3), 1 / 2),
+    [1 / 3, 1 / 3, 1 / 3]
+];